Effect of vaccination on household transmission of SARS-CoV-2 Delta variant of concern

Effective vaccines protect individuals by not only reducing the susceptibility to infection, but also reducing the infectiousness of breakthrough infections in vaccinated cases. To disentangle the vaccine effectiveness against susceptibility to infection (VES) and vaccine effectiveness against infectiousness (VEI), we took advantage of Danish national data comprising 24,693 households with a primary case of SARS-CoV-2 infection (Delta Variant of Concern, 2021) including 53,584 household contacts. In this setting, we estimated VES as 61% (95%-CI: 59-63), when the primary case was unvaccinated, and VEI as 31% (95%-CI: 26-36), when the household contact was unvaccinated. Furthermore, unvaccinated secondary cases with an infection exhibited a three-fold higher viral load compared to fully vaccinated secondary cases with a breakthrough infection. Our results demonstrate that vaccinations reduce susceptibility to infection as well as infectiousness, which should be considered by policy makers when seeking to understand the public health impact of vaccination against transmission of SARS-CoV-2.


S1 Background
This section provides some background statistics on the SARS-CoV-2 pandemic situation in Denmark, between June and November, 2021. Figure   In the study period, vaccinations were rolled out, going from below 40% fully vaccinated to more than 75% fully vaccinated individuals ( Figure S3). Denmark had a vaccination roll-out strategy that prioritized vulnerable people. Nursery home residents had highest prioritization (group 01), followed by citizens above age 65 who had the need of personal help and care (group 02), then older people above age 85 (group 03). The next three groups (04-06) contained employees in healthcare and social work, high-risk patients, and relatives of high-risk patients. The remaining population was subsequently prioritized based on birth year (groups 07-17). Naturally, this leads to a correlation between calendar time and vaccination status conditional on age. Figure S4 shows the proportion of each group being fully vaccinated from January to November, 2021. We see that the compliance is generally high, and fast roll-out is seen in all groups.
This roll-out strategy also meant that most of the vulnerable population was fully vacci-nated, when the Delta VOC was first detected in Denmark. For example, more than 90% of individuals above age 65 (group 09) were fully vaccinated. Finally, Denmark had relatively lenient restrictions during our study period. Figure S5 shows the government stringency index between June and November, 2021. The index is a composite measure of the strictness of policy responses and is based on nine response indicators including school closures, workplace closures, and travel bans. The index is calculated by the Oxford COVID-19 Government Response Tracker.

S1.1 Danish testing program
The Danish SARS-CoV-2 testing program is based on easily accessible testing that is free of charge. The use of testing has been broadly accepted by the public and by December 2021, more than 15% of the Danish population were RT-PCR tested each week and a similar percentage were antigen tested. Self-administered home tests only became widely used after our study period, by December 2021. There are three tracks in the testing

S2.1 Age-by-age transmission
To investigate the age-related transmission patterns, we split the data into 20-year age groups of both the primary cases and household contacts and estimated the secondary attack rate (SAR) between all combinations of age groups, stratified by vaccination status of both the primary case and household contacts ( Figure S6). Generally, the SAR was highest, when both the primary case and household contacts were unvaccinated (top-left panel

S2.2 Intra-household correlation of lineages
We found an overall intra-household correlation of SARS-CoV-2 lineages of 88% (95%-CI: 87-89) (Table S3), i.e., 88% of all secondary cases had the same sublineage of Delta as the primary case within the same household (conditional on the secondary test sample having a successfully sequenced genome). This intra-household correlation is lower compared to the one found in, e.g., Lyngse et al. 20 , at 96-99%. This could be because the society is more open, so there is a higher risk of community infection relative to household infection.
However, it could also be due to uncertainty in the classification of subtype lineages of the Delta VOC, which is changing over time. In the present study, we used PANGO Lineage classifications from 2021-11-10, why bias from temporal differences in the PANGO classifications were not an issue.
In the present study, there is potential bias in the intra-household correlation of lineages across vaccinated and unvaccinated individuals, which could invalidate our comparisons of the relative risks. Table S3 presents the intra-household correlation of lineages across all combinations of vaccinated and unvaccinated primary and secondary cases. We found no statistically significant difference across any of the combinations, so there is no evidence for differential bias across our groups of comparison.

S2.3 Correlation of vaccination status within households
Vaccination status among household members are likely correlated due to several reasons.
First, individuals are probably likely to live with other individuals with the same beliefs.
Thus individuals that are pro being vaccinated are more likely to live together with other individuals that also are pro being vaccinated-and vice versa. Second, individuals are likely to live with a partner around their own age. As vaccination eligibility is correlated with age, individuals are likely to be eligible for vaccination around the same time. Third, there may be a fixed cost of being vaccinated, e.g., transportation time to the vaccination place. Thus, households may pool their time of vaccination on the same day to minimize these costs. Figure S7 provides estimates of the correlation of the vaccination status between primary cases and contacts, stratified by ten year age groups. It clearly shows some correlation among household members. Among young children (<12 years) there is perfect correlation, as they were not eligible for being vaccinated. We found a correlation of 0.63 within the full sample and a correlation of 0.72, when restricting the sample to individuals above age 12. Notes: This figures provides estimates of the correlation of the vaccination status between primary cases and household contacts, stratified by ten-year age groups.

S2.4 Testing probabilities across vaccinated and unvaccinated individuals
When estimating the probability that an individual tests positive, it is conditional on the individual actually being tested. Selection bias is a potential concern, if the vaccination status of a household contact within the household is correlated with the probability of being tested after the identification of the primary case. Overall, we find that household contacts that are fully vaccinated are 7 percentage points (on a basis of 75%) more likely to be tested 1-14 days after exposure, compared to unvaccinated contacts (Table S8.a).
This suggests that there is a correlation between the vaccination status of the exposed contact and the compliance with being tested after exposure to a household primary case.
Panel (b) shows there are temporal differences in the propensity to be tested. These differences are highly correlated with the time of the school summer holiday. Panel (c) shows that there are differences across age groups in the propensity to be tested. Overall, we found that fully vaccinated household contacts were more likely to be tested after exposure to a primary case compared to unvaccinated contacts.

S2.5 Ct values for vaccinated vs unvaccinated cases
One concern in investigating the infectiousness among vaccinated and unvaccinated cases is that the viral load may differ across the two groups. Indeed the literature has shown that the viral load can be reduced for vaccinated individuals with breakthrough infections compared to unvaccinated individuals with infections 16 . We found that samples from vaccinated primary cases had a lower viral load distribution (higher Ct values) compared to samples from unvaccinated primary cases ( Figure S9). they believe they are less likely to be infected because of their vaccination status. We investigated this potential selection bias by comparing secondary cases that were fully vaccinated with unvaccinated secondary cases that tested positive on the same day after exposure of the primary case ( Figure 2 and Table S4). We found that unvaccinated secondary cases had a 1.6 point lower Ct value, which translates to a 3-fold higher viral load due to the doubling property of the Ct measurement (2 1.6 = 3) (Table S4, model II).

S2.6 Robustness of VE estimates
This section addresses the robustness of the VE estimates presented in Table 2.   Notes: This table provides VE estimates from the same model as Table 2, conditional on the household contacts having a test result. This table provides estimates of vaccine effectiveness (%) against susceptibility (V E S ) as a pooled estimate ("Pool") as well as stratified by whether the primary case was unvaccinated ("Not") or fully vaccinated ("Fully"). The estimates of vaccine effectiveness against infectiousness (V E I ) is given as a pooled estimate and stratified by the vaccination status of the contacts within the household. The total vaccine effectiveness (V E T ) is defined as both the primary case and contacts being vaccinated relative to them both being unvaccinated. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model.  Notes: This table provides VE estimates from the same model as Table 2, controlling for the sample Ct value of the primary case. This table provides estimates of vaccine effectiveness (%) against susceptibility (V E S ) as a pooled estimate ("Pool") as well as stratified by whether the primary case was unvaccinated ("Not") or fully vaccinated ("Fully"). The estimates of vaccine effectiveness against infectiousness (V E I ) is given as a pooled estimate and stratified by the vaccination status of the contacts within the household. The total vaccine effectiveness (V E T ) is defined as both the primary case and contacts being vaccinated relative to them both being unvaccinated. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. V E S for primary cases fully vaccinated only includes primary cases with a sample Ct value >20.  Notes: This table provides VE estimates from the same model as Table 2, controlling for the sample Ct value of the primary case, conditional on the household contacts having a test result. This table provides estimates of vaccine effectiveness (%) against susceptibility (V E S ) as a pooled estimate ("Pool") as well as stratified by whether the primary case was unvaccinated ("Not") or fully vaccinated ("Fully"). The estimates of vaccine effectiveness against infectiousness (V E I ) is given as a pooled estimate and stratified by the vaccination status of the contacts within the household. The total vaccine effectiveness (V E T ) is defined as both the primary case and contacts being vaccinated relative to them both being unvaccinated. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. VES for primary cases fully vaccinated only includes primary cases with a sample Ct value >20.  Notes: This table provides VE estimates from the same model as Table 2 by time since vaccination (bi-monthly). This table provides estimates of vaccine effectiveness (%) against susceptibility (V E S ) as a pooled estimate ("Pool") as well as stratified by whether the primary case was unvaccinated ("Not") or fully vaccinated ("Fully"). For V E S , time since vaccination is estimated for the household contacts. The estimates of vaccine effectiveness against infectiousness (V E I ) is given as a pooled estimate and stratified by the vaccination status of the contacts within the household. For V E I , time since vaccination is estimated for the primary cases. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. Note, the negative V E I estimates, when the household contacts were fully vaccinated, suggest that there is bias in the comparison of the vaccinated and unvaccinated population that we do not fully control for. We did not find negative V E I estimates, when we conditioned on the household contacts having a test result (Appendix Table S9), indicating that differences in the probability of being tested across unvaccinated and fully vaccinated contacts is a bias in our model (Appendix S2.4). Other behavioral biases across unvaccinated and fully vaccinated individuals are also likely. Thus it is most likely that there is a waning effect of vaccination, but it is very unlikely that the effect is negative.  Notes: This table provides VE estimates from the same model as Table 2 by time since vaccination (bi-monthly), conditional on the household contact having a test result. This table provides estimates of vaccine effectiveness (%) against susceptibility (V E S ) as a pooled estimate ("Pool") as well as stratified by whether the primary case was unvaccinated ("Not") or fully vaccinated ("Fully"). For V E S , time since vaccination is estimated for the household contacts. The estimates of vaccine effectiveness against infectiousness (V E I ) is given as a pooled estimate and stratified by the vaccination status of the contacts within the household. For V E I , time since vaccination is estimated for the primary cases. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model.

S3 Statistical Appendix
This section provides more details of the statistical methods used to generate the results presented in the main manuscript.
We defined the secondary attack rate (SAR) as the proportion of contacts that were infected within each household 1-14 days after exposure to a primary case. We only included individuals that were either fully vaccinated (V) or not vaccinated (N), thus excluding individuals that were partially vaccinated.
To compare attack rates across different vaccination status of primary cases and contacts, we estimated the relative risk (RR). The vaccine effectiveness (VE) is given by one minus the relative risk (1-RR) of the SAR of vaccinated individuals compared to the SAR of the unvaccinated individuals. We stratified our analyses in order to separate the VE of susceptibility to infection of the exposed contact (V E S ) from the VE of infectiousness in infected primary cases (V E I ), and to estimate the total VE (V E T ). In particular, we use the following 7 equations, with underlying estimates for SAR produced using generalized linear models that control for age, sex, household size, and calendar week, with standard errors clustered on the household level.
Let SAR (θp,θ i ) denote the SAR, where θ is the vaccination status θ ∈ {V, N } (Fully Vaccinated or Not vaccinated ) of primary cases (p) and contacts (i). Let "· " denote the pooled sample of both vaccination statuses. Thus, the pooled SAR is denoted as Vaccine effectiveness of susceptibility (V E S ) First, we compared the SAR across contacts that were fully vaccinated and contacts that were not vaccinated, unconditional of the vaccination status of the primary case.
The pooled VE of susceptibility to infection in exposed contacts (V E S ) is given by: i.e., the SAR of vaccinated contacts relative to the SAR of unvaccinated contactsunconditional on the vaccination status of the primary case.
Next, we hold the vaccination status of the primary case fixed, and again compare the SAR across contacts that are fully vaccinated and not vaccinated.
VE of susceptibility to infection in exposed contacts among unvaccinated primary cases is given by: VE of susceptibility to infection in exposed contacts among fully vaccinated primary cases is given by:

Vaccine effectiveness of infectiousness (V E I )
First, we compared the SAR across primary cases that were fully vaccinated and not vaccinated, unconditional of the vaccination status of the household contacts.
The pooled VE of infectiousness in primary cases (V E I ) is given by: V E I(V,·/N,·) = 1 − SAR (V,·) SAR (N,·) (4) Next, we hold the vaccination status of the contacts fixed, and compare the SAR across primary cases that are fully vaccinated and not vaccinated.
VE of infectiousness in primary cases among unvaccinated contacts is given by: VE of infectiousness in primary cases among fully vaccinated contacts is given by: Total vaccine effectiveness (V E T ) Finally, we compared the SAR, where both the primary case and contacts were fully vaccinated, with the SAR, where both the primary case and contacts were unvaccinated.
The total VE is given by:

Estimation
We estimated the relative risks for V E S , V E I and V E T using the following generalized linear model (GLM), with a Poisson distribution response and log link function: log(λ i,p ) = V acc + Age i + Age p + Sex i + Sex p + HouseholdSize p + W eek t , where V acc is a binary fixed effect representing one of the following explanatory variables for each model: -For V E S , V acc refers to vaccination status of the contact i.
-For V E I , V acc refers to vaccination status of the primary case p.
-For V E T , V acc refers to vaccination status of both the primary case and contacts p, i.
Age denotes categorical fixed effects of age group in 10 year intervals, Sex is a binary fixed effect controlling for sex, HouseholdSize denotes categorical fixed effects of the number of household members, and W eek is a categorical fixed effect of the calendar week t. Standard errors were clustered on the household level in order to control for within-household correlation in risk.
The GLM was fit using maximum likelihood in SAS. Note that the Poisson distribution is used with binary outcome in order to facilitate the calculation of relative risks.

Difference in Ct values for secondary cases
First, to investigate the dynamics of the difference in the Ct values across vaccinated and unvaccinated secondary cases, we estimated the difference in the Ct values across each day since exposure to the primary case, using the following equation: where τ is the time between the secondary case (i) and primary case (p) testing positive, which runs from 1 to 14; I τ is a vector of indicators of time since the primary case. V acc i is a dummy for the secondary case being fully vaccinated or unvaccinated. Age i is a vector of fixed effects for 5 year age groups.
Next, as we found no evidence of an interaction term between time since primary case and vaccination status, we proceeded with the simpler equation to estimate the difference in Ct values across vaccination status of the secondary case: Ct i,t = V acc i + τ I τ + Age i + Age p + V acc p + Ct p + ε i,t , where p denotes the primary case characteristics, and i the secondary case characteristics.